Design, the art of creating new inventions for addressing human needs, is a fundamental human drive that underpins our civilization and distinguishes us from other biological creatures. This drive has led to the invention of buildings, cities, clothes, food, technology and every artifact we make and use. Throughout history, there have been attempts to formalize a method of design so artifacts can be systematically invented. This type of thinking has led to formal systems in design. In architecture, we speak of the Greek ‘orders’, Alberti's system of proportions, Le Corbusier's ‘modulor’ or Matila Ghyka's use of the golden mean as the basis for the “geometry of art and life” (to name one of several such examples). These examples in art and architecture are the precursors of rule-based thinking as the logical next step in the evolution of design to the digital. Currently used rule-based form-generation techniques include fractals, L-systems based on Aristid Lindenmeyer's work on shape grammars for biological form like plants, cellular automata (especially John Conway's ‘game of life’ and Stephen Wolfram's ‘new kind of science’), and the artificial life (A-life) paradigm for generating evolution of form as an example of a digital model for how nature works.
Parallel to these form-generating systems, there have been examples of using morphology as a conceptual device for discovery and invention. Raymond Lull, the 12th century Catalan thinker used diagrams and constructions like concentric wheels which could be turned independently for deriving new combinations of concepts and information being represented in spokes or pie-segments of the wheel. The astrophysicist Fritz Zwicky in the 1960s used a cube to map entities along the 3 directions of space to combine the represented entities in new innovative ways as the mind zig-zagged its way through the cube. The designer William Katavolos, also in the 1960s, used 2- and 3 dimensional cubic matrices as a conceptual tool to invent new designs for products. The paleontologist David Raup, in 1965, used a 3-dimensional cube to define the space of all spiral forms of sea-shells including known ones and new fictitious ones. Haresh Lalvani, the author of the present invention, used higher-dimensional cubes for organizing and generating a variety of space structures like polyhedra, tilings, patterns and other structures.